%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:55:24 EDT 2023

% Result   : Theorem 43.17s 42.70s
% Output   : Proof 43.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 19:24:54 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 43.17/42.70  
% 43.17/42.70  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 43.17/42.70  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.17/42.70  %-----------------------------------------------------
% 43.17/42.70  ncf(matrix, plain, [(724 ^ _140864) ^ [_141185, _141187] : [727 ^ _140864 : [(732 ^ _140864) ^ [] : [-(712 ^ [] = ordered_pair(725 ^ [_141185, _141187], 726 ^ [_141185, _141187]))], (730 ^ _140864) ^ [] : [-(member(726 ^ [_141185, _141187], universal_class))], (728 ^ _140864) ^ [] : [-(member(725 ^ [_141185, _141187], universal_class))]], _141187 = 712 ^ [], _141185 = 712 ^ []], (714 ^ _140864) ^ [_140929, _140931] : [member(_140931, universal_class), member(_140929, universal_class), 712 ^ [] = ordered_pair(_140931, _140929)], !, (409 ^ _115613) ^ [_129882, _129884, _129886] : [-(restrict(_129884, _129886, _129882) = intersection(_129884, cross_product(_129886, _129882)))], (449 ^ _115613) ^ [_131365] : [-(subclass(rotate(_131365), cross_product(cross_product(universal_class, universal_class), universal_class)))], (552 ^ _115613) ^ [_134966, _134968] : [member(_134968, sum_class(_134966)), 556 ^ _115613 : [(559 ^ _115613) ^ [] : [-(member(555 ^ [_134966, _134968], _134966))], (557 ^ _115613) ^ [] : [-(member(_134968, 555 ^ [_134966, _134968]))]]], (431 ^ _115613) ^ [_130740, _130742, _130744, _130746] : [member(ordered_pair(ordered_pair(_130744, _130742), _130740), rotate(_130746)), 434 ^ _115613 : [(437 ^ _115613) ^ [] : [-(member(ordered_pair(ordered_pair(_130742, _130740), _130744), _130746))], (435 ^ _115613) ^ [] : [-(member(ordered_pair(ordered_pair(_130744, _130742), _130740), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (258 ^ _115613) ^ [_124692, _124694] : [260 ^ _115613 : [(263 ^ _115613) ^ [] : [member(259 ^ [_124692, _124694], _124692)], (261 ^ _115613) ^ [] : [-(member(259 ^ [_124692, _124694], _124694))]], -(subclass(_124694, _124692))], (325 ^ _115613) ^ [_127084, _127086, _127088, _127090] : [-(member(ordered_pair(_127090, _127088), cross_product(_127086, _127084))), member(_127090, _127086), member(_127088, _127084)], (585 ^ _115613) ^ [_136109, _136111] : [-(member(_136111, power_class(_136109))), member(_136111, universal_class), subclass(_136111, _136109)], (544 ^ _115613) ^ [] : [-(inductive(540 ^ []))], (335 ^ _115613) ^ [_127417, _127419] : [342 ^ _115613 : [(345 ^ _115613) ^ [] : [-(second(ordered_pair(_127419, _127417)) = _127417)], (343 ^ _115613) ^ [] : [-(first(ordered_pair(_127419, _127417)) = _127419)]], member(_127419, universal_class), member(_127417, universal_class)], (391 ^ _115613) ^ [_129333, _129335] : [member(_129333, complement(_129335)), 394 ^ _115613 : [(397 ^ _115613) ^ [] : [member(_129333, _129335)], (395 ^ _115613) ^ [] : [-(member(_129333, universal_class))]]], (126 ^ _115613) ^ [_119895, _119897, _119899, _119901] : [-(union(_119901, _119897) = union(_119899, _119895)), _119901 = _119899, _119897 = _119895], (222 ^ _115613) ^ [_123345, _123347] : [_123347 = _123345, -(singleton(_123347) = singleton(_123345))], (621 ^ _115613) ^ [_137407] : [member(_137407, identity_relation), 625 ^ _115613 : [(628 ^ _115613) ^ [] : [-(_137407 = ordered_pair(624 ^ [_137407], 624 ^ [_137407]))], (626 ^ _115613) ^ [] : [-(member(624 ^ [_137407], universal_class))]]], (98 ^ _115613) ^ [_118854, _118856] : [_118856 = _118854, -(second(_118856) = second(_118854))], (640 ^ _115613) ^ [_138088] : [function(_138088), 643 ^ _115613 : [(646 ^ _115613) ^ [] : [-(subclass(compose(_138088, inverse(_138088)), identity_relation))], (644 ^ _115613) ^ [] : [-(subclass(_138088, cross_product(universal_class, universal_class)))]]], (20 ^ _115613) ^ [_116361, _116363] : [-(inductive(_116361)), _116363 = _116361, inductive(_116363)], (30 ^ _115613) ^ [_116684, _116686, _116688, _116690] : [-(subclass(_116688, _116684)), subclass(_116690, _116686), _116690 = _116688, _116686 = _116684], (489 ^ _115613) ^ [_132847] : [-(successor(_132847) = union(_132847, singleton(_132847)))], (421 ^ _115613) ^ [_130363, _130365] : [-(member(_130363, domain_of(_130365))), member(_130363, universal_class), -(restrict(_130365, singleton(_130363), universal_class) = null_class)], (668 ^ _115613) ^ [_138956, _138958] : [disjoint(_138958, _138956), 671 ^ _115613 : [(672 ^ _115613) ^ [_139095] : [member(_139095, _138958), member(_139095, _138956)]]], (658 ^ _115613) ^ [_138624, _138626] : [-(member(image(_138624, _138626), universal_class)), member(_138626, universal_class), function(_138624)], (411 ^ _115613) ^ [_129973] : [member(_129973, null_class)], (611 ^ _115613) ^ [_137043, _137045, _137047, _137049] : [-(member(ordered_pair(_137045, _137043), compose(_137047, _137049))), member(_137045, universal_class), member(_137043, image(_137047, image(_137049, singleton(_137045))))], (353 ^ _115613) ^ [_128090, _128092] : [member(ordered_pair(_128092, _128090), element_relation), 356 ^ _115613 : [(359 ^ _115613) ^ [] : [-(member(_128092, _128090))], (357 ^ _115613) ^ [] : [-(member(_128090, universal_class))]]], (160 ^ _115613) ^ [_121154, _121156, _121158, _121160, _121162, _121164] : [-(restrict(_121164, _121160, _121156) = restrict(_121162, _121158, _121154)), _121164 = _121162, _121160 = _121158, _121156 = _121154], (277 ^ _115613) ^ [_125393, _125395] : [-(_125395 = _125393), subclass(_125395, _125393), subclass(_125393, _125395)], (373 ^ _115613) ^ [_128736, _128738, _128740] : [member(_128736, intersection(_128740, _128738)), 376 ^ _115613 : [(379 ^ _115613) ^ [] : [-(member(_128736, _128738))], (377 ^ _115613) ^ [] : [-(member(_128736, _128740))]]], (503 ^ _115613) ^ [_133364, _133366] : [-(member(ordered_pair(_133366, _133364), successor_relation)), member(_133366, universal_class), member(_133364, universal_class), successor(_133366) = _133364], (180 ^ _115613) ^ [_121860, _121862, _121864, _121866] : [-(cross_product(_121866, _121862) = cross_product(_121864, _121860)), _121866 = _121864, _121862 = _121860], (347 ^ _115613) ^ [_127825, _127827, _127829] : [member(_127825, cross_product(_127829, _127827)), -(_127825 = ordered_pair(first(_127825), second(_127825)))], (104 ^ _115613) ^ [_119072, _119074] : [_119074 = _119072, -(complement(_119074) = complement(_119072))], (648 ^ _115613) ^ [_138325] : [-(function(_138325)), subclass(_138325, cross_product(universal_class, universal_class)), subclass(compose(_138325, inverse(_138325)), identity_relation)], (248 ^ _115613) ^ [_124378, _124380] : [subclass(_124380, _124378), 251 ^ _115613 : [(252 ^ _115613) ^ [_124515] : [member(_124515, _124380), -(member(_124515, _124378))]]], (630 ^ _115613) ^ [_137712] : [-(member(_137712, identity_relation)), 631 ^ _115613 : [(632 ^ _115613) ^ [_137805] : [member(_137805, universal_class), _137712 = ordered_pair(_137805, _137805)]]], (58 ^ _115613) ^ [_117544, _117546] : [-(function(_117544)), _117546 = _117544, function(_117546)], (519 ^ _115613) ^ [_133822] : [-(range_of(_133822) = domain_of(inverse(_133822)))], (531 ^ _115613) ^ [_134286] : [-(inductive(_134286)), member(null_class, _134286), subclass(image(successor_relation, _134286), _134286)], (491 ^ _115613) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (4 ^ _115613) ^ [_115844, _115846] : [_115846 = _115844, -(_115844 = _115846)], (10 ^ _115613) ^ [_116048, _116050, _116052] : [-(_116052 = _116048), _116052 = _116050, _116050 = _116048], (687 ^ _115613) ^ [_139619] : [-(_139619 = null_class), 691 ^ _115613 : [(696 ^ _115613) ^ [] : [-(disjoint(690 ^ [_139619], _139619))], (694 ^ _115613) ^ [] : [-(member(690 ^ [_139619], _139619))], (692 ^ _115613) ^ [] : [-(member(690 ^ [_139619], universal_class))]]], (469 ^ _115613) ^ [_132156] : [-(subclass(flip(_132156), cross_product(cross_product(universal_class, universal_class), universal_class)))], (439 ^ _115613) ^ [_131033, _131035, _131037, _131039] : [-(member(ordered_pair(ordered_pair(_131037, _131035), _131033), rotate(_131039))), member(ordered_pair(ordered_pair(_131037, _131035), _131033), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_131035, _131033), _131037), _131039)], (678 ^ _115613) ^ [_139271, _139273] : [680 ^ _115613 : [(683 ^ _115613) ^ [] : [-(member(679 ^ [_139271, _139273], _139271))], (681 ^ _115613) ^ [] : [-(member(679 ^ [_139271, _139273], _139273))]], -(disjoint(_139273, _139271))], (701 ^ _115613) ^ [] : [-(function(699 ^ []))], (212 ^ _115613) ^ [_123014, _123016, _123018, _123020] : [-(image(_123020, _123016) = image(_123018, _123014)), _123020 = _123018, _123016 = _123014], (287 ^ _115613) ^ [_125737, _125739, _125741] : [member(_125741, unordered_pair(_125739, _125737)), 290 ^ _115613 : [(293 ^ _115613) ^ [] : [-(_125741 = _125739), -(_125741 = _125737)], (291 ^ _115613) ^ [] : [-(member(_125741, universal_class))]]], (148 ^ _115613) ^ [_120662, _120664] : [_120664 = _120662, -(domain_of(_120664) = domain_of(_120662))], (317 ^ _115613) ^ [_126819, _126821, _126823, _126825] : [member(ordered_pair(_126825, _126823), cross_product(_126821, _126819)), 320 ^ _115613 : [(323 ^ _115613) ^ [] : [-(member(_126823, _126819))], (321 ^ _115613) ^ [] : [-(member(_126825, _126821))]]], (603 ^ _115613) ^ [_136762, _136764, _136766, _136768] : [member(ordered_pair(_136764, _136762), compose(_136766, _136768)), 606 ^ _115613 : [(609 ^ _115613) ^ [] : [-(member(_136762, image(_136766, image(_136768, singleton(_136764)))))], (607 ^ _115613) ^ [] : [-(member(_136764, universal_class))]]], (577 ^ _115613) ^ [_135868, _135870] : [member(_135870, power_class(_135868)), 580 ^ _115613 : [(583 ^ _115613) ^ [] : [-(subclass(_135870, _135868))], (581 ^ _115613) ^ [] : [-(member(_135870, universal_class))]]], (68 ^ _115613) ^ [_117847, _117849, _117851, _117853] : [-(member(_117851, _117847)), member(_117853, _117849), _117853 = _117851, _117849 = _117847], (44 ^ _115613) ^ [_117128, _117130, _117132, _117134] : [-(disjoint(_117132, _117128)), disjoint(_117134, _117130), _117134 = _117132, _117130 = _117128], (174 ^ _115613) ^ [_121614, _121616] : [_121616 = _121614, -(power_class(_121616) = power_class(_121614))], (206 ^ _115613) ^ [_122768, _122770] : [_122770 = _122768, -(sum_class(_122770) = sum_class(_122768))], (200 ^ _115613) ^ [_122550, _122552] : [_122552 = _122550, -(inverse(_122552) = inverse(_122550))], (142 ^ _115613) ^ [_120444, _120446] : [_120446 = _120444, -(flip(_120446) = flip(_120444))], (451 ^ _115613) ^ [_131531, _131533, _131535, _131537] : [member(ordered_pair(ordered_pair(_131537, _131535), _131533), flip(_131531)), 454 ^ _115613 : [(457 ^ _115613) ^ [] : [-(member(ordered_pair(ordered_pair(_131535, _131537), _131533), _131531))], (455 ^ _115613) ^ [] : [-(member(ordered_pair(ordered_pair(_131537, _131535), _131533), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (110 ^ _115613) ^ [_119318, _119320, _119322, _119324] : [-(intersection(_119324, _119320) = intersection(_119322, _119318)), _119324 = _119322, _119320 = _119318], (561 ^ _115613) ^ [_135277, _135279] : [-(member(_135279, sum_class(_135277))), 562 ^ _115613 : [(563 ^ _115613) ^ [_135371] : [member(_135279, _135371), member(_135371, _135277)]]], (517 ^ _115613) ^ [_133735] : [-(inverse(_133735) = domain_of(flip(cross_product(_133735, universal_class))))], (399 ^ _115613) ^ [_129575, _129577] : [-(member(_129575, complement(_129577))), member(_129575, universal_class), -(member(_129575, _129577))], (546 ^ _115613) ^ [_134731] : [inductive(_134731), -(subclass(540 ^ [], _134731))], (92 ^ _115613) ^ [_118636, _118638] : [_118638 = _118636, -(first(_118638) = first(_118636))], (698 ^ _115613) ^ [_140029, _140031] : [-(apply(_140031, _140029) = sum_class(image(_140031, singleton(_140029))))], (471 ^ _115613) ^ [_132308, _132310, _132312] : [member(_132308, union(_132312, _132310)), -(member(_132308, _132312)), -(member(_132308, _132310))], (542 ^ _115613) ^ [] : [-(member(540 ^ [], universal_class))], (267 ^ _115613) ^ [_125020] : [-(subclass(_125020, universal_class))], (521 ^ _115613) ^ [_133920, _133922] : [-(image(_133920, _133922) = range_of(restrict(_133920, _133922, universal_class)))], (190 ^ _115613) ^ [_122219, _122221, _122223, _122225] : [-(compose(_122225, _122221) = compose(_122223, _122219)), _122225 = _122223, _122221 = _122219], (595 ^ _115613) ^ [_136400] : [member(_136400, universal_class), -(member(power_class(_136400), universal_class))], (228 ^ _115613) ^ [_123591, _123593, _123595, _123597] : [-(apply(_123597, _123593) = apply(_123595, _123591)), _123597 = _123595, _123593 = _123591], (381 ^ _115613) ^ [_128987, _128989, _128991] : [-(member(_128987, intersection(_128991, _128989))), member(_128987, _128991), member(_128987, _128989)], (136 ^ _115613) ^ [_120226, _120228] : [_120228 = _120226, -(successor(_120228) = successor(_120226))], (269 ^ _115613) ^ [_125156, _125158] : [_125158 = _125156, 272 ^ _115613 : [(275 ^ _115613) ^ [] : [-(subclass(_125156, _125158))], (273 ^ _115613) ^ [] : [-(subclass(_125158, _125156))]]], (493 ^ _115613) ^ [_133043, _133045] : [member(ordered_pair(_133045, _133043), successor_relation), 496 ^ _115613 : [(501 ^ _115613) ^ [] : [-(successor(_133045) = _133043)], (499 ^ _115613) ^ [] : [-(member(_133043, universal_class))], (497 ^ _115613) ^ [] : [-(member(_133045, universal_class))]]], (2 ^ _115613) ^ [_115737] : [-(_115737 = _115737)], (313 ^ _115613) ^ [_126543] : [-(singleton(_126543) = unordered_pair(_126543, _126543))], (601 ^ _115613) ^ [_136593, _136595] : [-(subclass(compose(_136593, _136595), cross_product(universal_class, universal_class)))], (703 ^ _115613) ^ [_140229] : [member(_140229, universal_class), -(_140229 = null_class), -(member(apply(699 ^ [], _140229), _140229))], (238 ^ _115613) ^ [_123930, _123932, _123934, _123936] : [-(ordered_pair(_123936, _123932) = ordered_pair(_123934, _123930)), _123936 = _123934, _123932 = _123930], (571 ^ _115613) ^ [_135631] : [member(_135631, universal_class), -(member(sum_class(_135631), universal_class))], (311 ^ _115613) ^ [_126460, _126462] : [-(member(unordered_pair(_126462, _126460), universal_class))], (315 ^ _115613) ^ [_126640, _126642] : [-(ordered_pair(_126642, _126640) = unordered_pair(singleton(_126642), unordered_pair(_126642, singleton(_126640))))], (413 ^ _115613) ^ [_130109, _130111] : [member(_130109, domain_of(_130111)), 416 ^ _115613 : [(419 ^ _115613) ^ [] : [restrict(_130111, singleton(_130109), universal_class) = null_class], (417 ^ _115613) ^ [] : [-(member(_130109, universal_class))]]], (523 ^ _115613) ^ [_134053] : [inductive(_134053), 526 ^ _115613 : [(529 ^ _115613) ^ [] : [-(subclass(image(successor_relation, _134053), _134053))], (527 ^ _115613) ^ [] : [-(member(null_class, _134053))]]], (361 ^ _115613) ^ [_128333, _128335] : [-(member(ordered_pair(_128335, _128333), element_relation)), member(_128333, universal_class), member(_128335, _128333)], (82 ^ _115613) ^ [_118305, _118307, _118309, _118311] : [-(unordered_pair(_118311, _118307) = unordered_pair(_118309, _118305)), _118311 = _118309, _118307 = _118305], (120 ^ _115613) ^ [_119649, _119651] : [_119651 = _119649, -(rotate(_119651) = rotate(_119649))], (459 ^ _115613) ^ [_131824, _131826, _131828, _131830] : [-(member(ordered_pair(ordered_pair(_131830, _131828), _131826), flip(_131824))), member(ordered_pair(ordered_pair(_131830, _131828), _131826), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_131828, _131830), _131826), _131824)], (371 ^ _115613) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (299 ^ _115613) ^ [_126082, _126084, _126086] : [-(member(_126086, unordered_pair(_126084, _126082))), member(_126086, universal_class), 304 ^ _115613 : [(307 ^ _115613) ^ [] : [_126086 = _126082], (305 ^ _115613) ^ [] : [_126086 = _126084]]], (154 ^ _115613) ^ [_120880, _120882] : [_120882 = _120880, -(range_of(_120882) = range_of(_120880))], (481 ^ _115613) ^ [_132576, _132578, _132580] : [482 ^ _115613 : [(485 ^ _115613) ^ [] : [member(_132576, _132578)], (483 ^ _115613) ^ [] : [member(_132576, _132580)]], -(member(_132576, union(_132580, _132578)))]], input).
% 43.17/42.70  ncf('1',plain,[732 : -(712 ^ [] = ordered_pair(725 ^ [712 ^ [], 712 ^ []], 726 ^ [712 ^ [], 712 ^ []])), 732 : 712 ^ [] = 712 ^ [], 732 : 712 ^ [] = 712 ^ []],start(724 ^ 0,bind([[_141185, _141187], [712 ^ [], 712 ^ []]]))).
% 43.17/42.70  ncf('1.1',plain,[712 ^ [] = ordered_pair(725 ^ [712 ^ [], 712 ^ []], 726 ^ [712 ^ [], 712 ^ []]), member(725 ^ [712 ^ [], 712 ^ []], universal_class), member(726 ^ [712 ^ [], 712 ^ []], universal_class)],extension(714 ^ 3,bind([[_140929, _140931], [726 ^ [712 ^ [], 712 ^ []], 725 ^ [712 ^ [], 712 ^ []]]]))).
% 43.17/42.70  ncf('1.1.1',plain,[-(member(725 ^ [712 ^ [], 712 ^ []], universal_class))],extension(728 ^ 4)).
% 43.17/42.70  ncf('1.1.2',plain,[-(member(726 ^ [712 ^ [], 712 ^ []], universal_class))],extension(730 ^ 4)).
% 43.17/42.70  ncf('1.2',plain,[-(712 ^ [] = 712 ^ []), 712 ^ [] = 712 ^ []],extension(4 ^ 1,bind([[_115844, _115846], [712 ^ [], 712 ^ []]]))).
% 43.17/42.70  ncf('1.2.1',plain,[-(712 ^ [] = 712 ^ [])],extension(2 ^ 2,bind([[_115737], [712 ^ []]]))).
% 43.17/42.70  ncf('1.3',plain,[-(712 ^ [] = 712 ^ []), 712 ^ [] = 712 ^ []],extension(4 ^ 1,bind([[_115844, _115846], [712 ^ [], 712 ^ []]]))).
% 43.17/42.70  ncf('1.3.1',plain,[-(712 ^ [] = 712 ^ [])],extension(2 ^ 2,bind([[_115737], [712 ^ []]]))).
% 43.17/42.70  %-----------------------------------------------------
% 43.17/42.70  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------